Divisibility and cellular automata

Cellular automata (CA) are perfect feedback machines which change the state of their cells step by step. In a certain sense, Pascalʹs triangle was the first CA and there is a strong connection between Pascalʹs triangle and the fractal pattern formation known as Sierpinski gasket. Generalizing divisibility properties of the coefficients of Pascalʹs triangle, binomial arrays as well as gaussian arrays are evaluated mod p. In these arrays, two fractal geometric characteristics are evident: a) self-similarity and b) non integer dimension. The conclusions at which we arrive,as well as the conjectures we propose, are important facts to take into account when modelling real experiments like catalytic oxidation reactions in Chemistry, where the remarkable resemblance of the graph: number of entries in the kth row of the Pascalʹs triangle which are not divisible by 2 vs k and the measurement of the chemical reaction rate as a function of time, provides the reason to model a catalytic converter by a one-dimensional CA [4].